Standard intuition in a multiple buyers‐single seller framework suggests that the buyer who is willing to pay the most for an object under sale would acquire it not only under a take‐it‐or‐leave‐it (TOLI) selling mechanism but also under bargaining with the seller, assuming of course that the buyers are not differentiated in terms of bargaining power. In this note we present a frequently encountered model where this principle fails to hold. We consider a Cournot market with two asymmetric firms, which are the potential buyers of a license to the use of a cost‐reducing technology. We compare the licensing outcome of the optimal TOLI mechanism with the outcome of a bargaining procedure. Surprisingly, we show that although the inefficient firm obtains the license under the optimal TOLI licensing mechanism, the result is reversed under bargaining, namely the efficient firm acquires it. As a byproduct, we obtain that market efficiency is lower under bargaining than under the optimal TOLI mechanism.